Mrs. Pearce is concerned about the swearing of Higgins when he speaks and his table manners when he eats because they now have an impressionable young "lady" living with them. She also tells Higgins he can't treat people like objects "as if you were picking up a pebble on the beach". She also questions Higgins as to the "terms" of Eliza's stay with them. She asks if she will be given any money, warning him to look ahead when the experiment is over.
Mrs. Pearce also asks Higgins not to come to breakfast just wearing his "dressing-gown", or at least not to use it as a napkin while he's eating. She's truly concerned about Higgins setting a good example for Eliza. Before she leaves the room, she tells Higgins not to "say anything to make the girl conceited about herself".
Overall, Mrs. Pearce is an informal "Pygmalion", even though Higgins is the predominant one. She works on Eliza's appearance and manners. Even though she's middle-class, she is aware of what proper behavior should be. She eventually develops a bond with Eliza, often having to defend her from Higgins.
Although Mrs. Pearce seems very snobbish at first, and not at all thrilled to have Eliza in the house, she has a kind heart and is a good person. What is more, it is she who treats Liza as a human being, with feelings and a future to consider, not just an experiment.
In Act II, Mrs. Pearce proves her concern by pleading with Higgins to consider what will happen to Eliza after the experiment concludes and they no longer have any use for her.